Timescales of excited state relaxation in $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ observed by time-resolved two-photon photoemission spectroscopy

The nonequilibrium properties of strongly correlated materials present a target in the search for new phases of matter. It is important to observe the types of excitations that exist in these materials and their associated relaxation dynamics. We have studied the photoexcitations in a spin-orbit assisted Mott insulator $\alpha \text{−}\mathrm{Ru}{\mathrm{Cl}}_3$ using time-resolved two-photon photoemission spectroscopy and transient reflection spectroscopy. We find that photoexcited carriers (doublons) in the upper Hubbard band rapidly relax to Mott-Hubbard excitons on a timescale of less than 200 fs. Subsequently, further relaxation of these lower-energy quasiparticles occurs with an energy-dependent time constant of that ranges from 370 to 600 fs due to exciton cooling. The population of Mott-Hubbard excitons persists for timescales up to several microseconds.

Figure 1

(a) Background-subtracted 2PPE band map of the UHB region measured with a pump energy of 2.5 eV and a probe of 6.2 eV. (b) 1PPE spectrum measured with 21.2-eV radiation. The energy gap is labeled as the approximate difference between the band edges.

Figure 2

(a) 2PPE spectra at different pump-photon energies showing the population of the UHB. (b) 2PPE energy distribution curve (EDC) at the zone center for a 2.5-eV pump energy showing the secondary background. Inset: the full energy spectrum showing the secondary electron cutoff. (c) Background-subtracted 2PPE spectra in the region of the UHB for the photon energies in (a). (d) Background-subtracted 2PPE spectra for different pump fluences at 2.5 eV. Colored lines are the data and the black lines are fits to the thermal line shape with hot electron temperatures indicated in the legend.

Figure 3

(a) Theoretical density of states for the UHB calculated using DMFT. (b) Calculated equilibrium occupation function at different temperatures for this model. (c) Connection between DMFT calculations and thermalized UHB population is made by showing the 2PPE data measured at 2.5-eV pump (red crosses) divided by the fitted DOS. The solid line shows the corresponding equilibrium DMFT occupation divided by the DOS at $T=1700\mathrm{K}$ from (b). The points are experimental data [raw 2PPE intensity divided by the best-fit DOS function A(E) from Fig. 2] with a hot electron temperature of 1590 K.

Figure 4

(a) Photoelectron intensity map as a function of energy and pump-probe delay time for 2.5-eV pump energy; the population in the UHB region is seen to decay very rapidly. (b) Horizontal cut through the UHB and MHE regions. The UHB (cyan) shows a nearly symmetric time trace that implies a population decay of less than 200 fs The MHE (red) shows an asymmetric trace with a time constant of ∼300 fs, determined by the fit to an exponentially modified Gaussian (black). The inset shows the population of the MHE at longer delays extending the time axis of the main plot out to ∼8 ps.

Figure 5

Differential reflectivity at 1.15 eV due to 3.1-eV pump excitation at different pump fluences.

Figure 6

Schematic illustration of the energy scales and relaxation timescales of the important photoexcitations revealed in our experiments. The pink ovals represent doublons which are transiently created in the UHB. In addition, the blue ovals show the corresponding holes created in the LHB (not directly observed in our experiments). The free carriers rapidly evolve to MHEs through Coulomb binding of doublons to holons. After a brief population relaxation by energy transfer to other degrees of freedom (exciton cooling) the MHEs persist for very long times $\left(>500\mathrm{ps}\right)$.